We develop a tensor-network surrogate for option pricing, targeting large-scale portfolio revaluation problems arising in market risk management (e.g., VaR and Expected Shortfall computations). The method involves representing high-dimensional price surfaces in tensor-train (TT) form using TT-cross approximation, constructing the surrogate directly from black-box price evaluations without materializing the full training tensor. For inference, we use a Laplacian kernel and derive TT representations of the kernel matrix and its closed-form inverse in the noise-free setting, enabling TT-based Gaussian process regression without dense matrix factorization or iterative linear solves. We found that hyperparameter optimization consistently favors a large kernel length-scale and show that in this regime the GPR predictor reduces to multilinear interpolation for off-grid inputs; we also derive a low-rank TT representation for this limit. We evaluate the approach on five-asset basket options over an eight dimensional parameter space (asset spot levels, strike, interest rate, and time to maturity). For European geometric basket puts, the tensor surrogate achieves lower test error at shorter training times than standard GPR by scaling to substantially larger effective training sets. For American arithmetic basket puts trained on LSMC data, the surrogate exhibits more favorable scaling with training-set size while providing millisecond-level evaluation per query, with overall runtime dominated by data generation.

翻译：我们针对市场风险管理（如VaR和预期亏损计算）中大规模投资组合重估价问题，开发了一种用于期权定价的张量网络代理模型。该方法采用张量训练（TT）形式的TT-cross近似来表征高维价格曲面，直接通过黑箱价格评估构建代理模型，无需实例化完整训练张量。在推理阶段，我们使用拉普拉斯核函数，并推导出无噪声设定下核矩阵及其闭式逆的TT表示，从而无需稠密矩阵分解或迭代线性求解即可实现基于TT的高斯过程回归。研究发现超参数优化始终倾向于大核长度尺度，并证明在该区间内GPR预测器退化为离网输入的多线性插值；我们还推导了该极限情况下的低秩TT表示。该方法在八维参数空间（资产即期价格水平、执行价、利率和到期时间）中针对五资产篮子期权进行评估。对于欧式几何篮子看跌期权，该张量代理模型通过扩展到显著更大的有效训练集，在更短训练时间内实现了低于标准GPR的测试误差。对于基于LSMC数据训练的美式算术篮子看跌期权，该代理模型在提供毫秒级单次查询评估的同时，展现出更优的训练集规模可扩展性，整体运行时间主要由数据生成阶段主导。